I approach home of hawk, say, with serious intent (2,7)
I believe the answer is:
in earnest
'with serious intent' is the definition.
(I've seen this before)
'i approach home' is the wordplay.
'approach' becomes 'near' (synonyms).
'home' becomes 'nest' (a bird's home).
'i'+'near'+'nest'='IN EARNEST'
'of hawk say' is the link.
This may not be right. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for in earnest that I've seen before include "with sincere intentions" , "Sincere in intention" , "with enthusiasm" , "with serious intent" , "With serious intention, not fooling about (2.7)" .)